Numerical simulation method for calculating effective viscosity of polymer under high temperature conditionTechnical Field
The invention relates to numerical simulation of oil reservoirs, in particular to a numerical simulation method for calculating effective viscosity of a polymer under high temperature conditions.
Background
Polymer flooding is one of the dominant technologies for improving crude oil recovery rate by chemical flooding in China, and is most mature and effective in various technologies for tertiary oil recovery. The main mechanism of the polymer flooding technology is to add a high-viscosity polymer into water injected into an oil reservoir, increase the viscosity of a flooding phase, and reduce the mobility ratio of the flooding fluid to the displaced fluid, so that the swept volume is enlarged. Some reservoirs driven by polymer in China are high-temperature high-salt reservoirs, the temperature is above 75 ℃, such as victory oil field, henan oil field and the like, and after the polymer is injected into the oil layer, thermal degradation can occur under the high-temperature condition, and the degradation can lead to breakage of polymer molecular chains, degradation into a small molecular structure and reduction of polymer solution viscosity.
Liu Xiangan, jiang Hanqiao, li Junjian, zhao Lin et al have established partial differential description equations of polymer viscosity changes for numerical simulation of polymer thermal stability, by which polymer thermal degradation processes of polymers in reservoir flows are simulated and calculated ([ 1] Liu Xiangan, jiang Hanqiao, luo Gongxia, et al, polymer thermal degradation numerical simulation based on viscosity correction model [ J ]. Daqing petroleum geology and development, 2015,34 (6): 95-99.[2] Li Junjian, jiang Hanqiao, liu Xiangan, et al, new search for polymer solution aging mathematical model under reservoir conditions [ J ]. Petroleum drilling process, 2016,38 (4): 499-544.)
Lin Chunyang, zhang Xiansong, liu Huiqing et al propose a "time flux" concept for numerical modeling of polymer thermal stability, thereby creating a reservoir numerical model that takes into account polymer aging effects. The main idea is to determine the equivalent aging time of the mixed polymers in the grid of the reservoir numerical simulation. ([ 3] Lin Chunyang, zhang Xiansong, liu Huiqing. Polymer solution aging action numerical model study [ J ]. Oil and gas theory, 2012,34 (12): 143-147 ] [4] Lin Chunyang, xue Xinsheng, zhu, et al. Polymer solution aging law under reservoir flow conditions and application [ J ]. Oil and gas geology and recovery ratio, 2013,20 (1): 77-80.).
In mathematical model description of oil reservoir numerical simulation software, except for shearing action in the flowing process, the change of polymer viscosity is generally reflected by the change of polymer concentration, however, when the polymer is degraded at high temperature, the concentration of the polymer is not changed, but is only degraded into small molecules by macromolecules, and the conventional oil reservoir numerical simulation model does not consider the influence of temperature, so that the thermal degradation mechanism of the polymer cannot be embodied in the conventional oil reservoir numerical simulation software, and further, the effective viscosity of the polymer under the high temperature condition of an oil reservoir cannot be accurately calculated, so that a scheme prediction index obtained based on a numerical simulation calculation result is more optimistic than the actual situation, and effective guidance is difficult to form for actual development of a mine.
The published relevant documents are focused on the study of static state thermal stability of the polymer, wherein the viscosity of the polymer changes along with the change of time under the high-temperature condition, complex influences caused by flow and diffusion of the polymer under the oil reservoir condition are not considered, particularly, influences of inflow and outflow of the polymer and thermal degradation of the polymer at different moments in a numerical simulation grid on the viscosity of a polymer mixed solution of the grid are not considered, or equivalent models which do not meet conservation laws or cannot be verified through experiments are adopted, so that the effective realization in numerical simulation software is difficult, for example, the convective diffusion equation of the viscosity established in documents [1-2] does not meet the physical conservation laws, the physical significance of the convective diffusion equation is to be further verified, and the conservation of the total aging time in documents [3-4] is difficult to be verified through experiments.
Disclosure of Invention
The invention mainly aims at a numerical simulation method for calculating effective viscosity of a polymer under a high-temperature condition, solves the problems that the thermal stability change of the polymer under a high-temperature static state is considered, the viscosity change of different positions at different moments under a polymer flowing state is reflected, meanwhile, a mathematical model meets the mass conservation, and related parameters can be obtained through an indoor experimental test result and are easy to realize in the existing oil reservoir numerical simulation software.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
The invention provides a numerical simulation method for calculating effective viscosity of a polymer under high temperature conditions, which comprises the following steps:
step 1, performing thermal degradation experiments on a polymer, and fitting according to experimental results to obtain a first-order degradation equation;
step 2, establishing a decay equation of the effective concentration of the polymer, and determining a decay coefficient of the effective concentration of the polymer;
Step 3, establishing an effective concentration equation of the polymer;
And 4, solving the equation in the step 3 to obtain the effective concentration of the polymer, and performing interpolation calculation according to the effective concentration and the polymer concentration-viscosity relation curve data obtained by testing.
Preferably, in step 1, the polymer is placed in an indoor high temperature environment, the viscosity of the polymer is measured for different time periods, a polymer solution time-viscosity curve is drawn, a first-order thermal degradation equation of the polymer viscosity is obtained through curve regression, and the thermal degradation coefficient of the viscosity is determined.
Further preferably, the first order thermal degradation equation for polymer viscosity can be expressed as:
preferably, the analytical solution of equation (1) is expressed as:
Where μ represents the viscosity of the polymer solution, μ0 represents the viscosity at the initial time of the polymer solution, t represents time, t0 represents time at the initial time, and λ represents the thermal degradation coefficient of the polymer.
Preferably, in step 2, the polymer concentration-viscosity relation curve and the viscosity degradation equation in step 1 are obtained according to an indoor experimental test, the viscosity change caused by thermal degradation of the polymer is equivalent to the attenuation of the effective concentration of the polymer, and the decay equation and the decay coefficient of the effective concentration of the polymer are determined.
Further preferably, the polymer solution effective concentration decay equation can be expressed as:
the analytical solution of equation (3) is expressed as:
Wherein Cp represents the effective concentration of the polymer solution, Cp0 represents the concentration at the initial time of the polymer solution, t represents time, t0 represents time at the initial time, and λp represents the decay factor of the effective concentration of the polymer.
Preferably, in step 3, the effective concentration equation for the polymer is established in the form:
Where φ represents porosity, ρp represents polymer density, Dp is diffusion coefficient, vw represents flow rate of aqueous phase, and Qp is source sink term.
Preferably, the equation in the step 3 is solved by using a finite difference algorithm to obtain the effective concentration of the polymer at each time and each space position, and then interpolation calculation is performed according to the effective concentration and the polymer concentration-viscosity curve data obtained by the indoor experimental test in the step 2, so that the effective viscosity after polymer flow, diffusion and high-temperature thermal degradation can be obtained.
The numerical simulation method for calculating the effective viscosity of the polymer under the high-temperature condition not only considers the change rule of the polymer viscosity along with time in a static state, but also considers the compound influence of the flow and diffusion of the polymer at different time and different space positions on the polymer solution viscosity, and meanwhile, the original polymer concentration calculation result is not changed, and the influence of various comprehensive factors on the effective viscosity of the polymer is reflected only by adding one effective polymer concentration equation. In addition, all formula parameters or data can be obtained through regression or interpolation of indoor experimental test data, the effective concentration equation of the polymer is a common convection diffusion equation in chemical flooding numerical simulation, a mature solving method can be applied to calculate, corresponding simulation functions are rapidly realized in the existing oil reservoir numerical simulation software, prediction of development effects and optimization of development schemes are effectively supported, and the method has good technical application prospect and supporting effect.
Compared with the prior art, the invention has the following excellent effects:
According to the invention, the influence of high-temperature thermal degradation on the viscosity of the polymer under the combined action of static and flowing states is comprehensively reflected by establishing the effective concentration equation of the polymer, all parameters and data can be obtained through indoor experiments, the equation accords with the basic physical law, and the equation is easy to solve and can be accurately and rapidly applied to oil reservoir numerical simulation software.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a graph of polymer viscosity as a function of time for thermal degradation in an embodiment of the invention;
FIG. 2 is a graph of polymer concentration versus viscosity experimental testing in an embodiment of the invention;
FIG. 3 is a graph of the effective concentration decay of a polymer in an embodiment of the present invention;
FIG. 4 is a graph showing the effect of thermal degradation coefficients of different polymers on the results of chemical flooding simulation in accordance with one embodiment of the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular forms also are intended to include the plural forms unless the context clearly indicates otherwise, and furthermore, it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, and/or combinations thereof.
In order to enable those skilled in the art to more clearly understand the technical scheme of the present invention, the technical scheme of the present invention will be described in detail with reference to specific embodiments.
Term interpretation:
The polymer effective concentration is the concentration of the polymer effective component which is equivalent to the change of the polymer effective component affecting the solution viscosity, namely the concentration of the polymer effective component, because the actual concentration of the polymer solution is not changed after thermal degradation and the change of the viscosity is caused by the reduction of the polymer molecular weight due to high temperature.
Example A numerical simulation method for calculating effective viscosity of a polymer at high temperature
The method comprises the following steps:
And step1, carrying out a thermal degradation experiment on the polymer, fitting according to an experimental result to obtain a first-order degradation equation, namely placing the polymer in an indoor high-temperature environment, measuring the viscosity of the polymer in different time periods, drawing a polymer solution time-viscosity curve, obtaining the first-order thermal degradation equation of the polymer viscosity through curve regression, and determining the thermal degradation coefficient of the viscosity.
The first order thermal degradation equation for polymer viscosity can be expressed as:
The analytical solution of equation (1) is expressed as:
Where μ represents the viscosity of the polymer solution, μ0 represents the viscosity at the initial time of the polymer solution, t represents time, t0 represents time at the initial time, and λ represents the thermal degradation coefficient of the polymer. FIG. 1 is a graph showing the viscosity of a polymer as a function of thermal degradation time, and from the results of FIG. 1, it can be seen that the thermal degradation coefficient of the viscosity of the polymer at 85℃is 0.011.
And 2, establishing a polymer effective concentration decay equation, determining a decay coefficient of the polymer effective concentration, namely obtaining a polymer concentration-viscosity relation curve and a viscosity degradation equation in the step 1 according to an indoor experimental test, equating the viscosity change caused by polymer thermal degradation to the decay of the polymer effective concentration, and determining the decay equation and the decay coefficient of the polymer effective concentration.
The effective concentration decay equation for a polymer solution can be expressed as:
the analytical solution of equation (3) is expressed as:
Wherein Cp represents the effective concentration of the polymer solution, Cp0 represents the concentration at the initial time of the polymer solution, t represents time, t0 represents time at the initial time, and λp represents the decay factor of the effective concentration of the polymer.
And 3, establishing a polymer effective concentration equation, namely combining the polymer effective concentration decay equation (3) in the step 2 with a mass conservation law, and establishing the polymer effective concentration equation in the form of:
Where φ represents porosity, ρp represents polymer density, Dp is diffusion coefficient, vw represents flow rate of aqueous phase, and Qp is source sink term.
FIG. 2 is a graph of polymer concentration versus viscosity test, and from the results of FIGS. 1 and 2, a two-dimensional interpolation is performed to obtain a decay curve of the effective polymer concentration over time, as shown in FIG. 3, while a decay equation of the effective polymer concentration can be regressed from the data points of FIG. 3, and as can be seen from FIG. 3, the decay coefficient of the effective polymer concentration is 0.009.
And 4, solving the equation (5) in the step 3 by utilizing a finite difference algorithm to obtain the effective concentration of the polymer at each time and each space position, and carrying out interpolation calculation according to the effective concentration and the polymer concentration-viscosity curve data obtained by the indoor experimental test in the step2 to obtain the effective viscosity after polymer flow, diffusion and high-temperature thermal degradation.
And (3) establishing an oil reservoir conceptual model, wherein the grid step length of the model in the directions of x, y and z is 5m multiplied by 5m, and the grid scale is 20 multiplied by 1. The plane permeability is 2 mu m2, two wells are produced by one injection, the I1 well is a quantitative injection well, the grid coordinates of well points are (1, 1), the daily injection amount is 20m3, the P1 well is a constant liquid production well, the grid coordinates of well points are (20, 20), and the injection-production ratio is 1:1. The simulation time is 3000 days, the injection slug is set to be 1650 days to 2000 days, the polymer with the concentration of 1000mg/L and the surfactant with the concentration of 0.2 percent are injected, and the rest time is water flooding.
Fig. 4 is a numerical simulation result corresponding to different polymer viscosity thermal degradation coefficients calculated based on a conceptual model, where under the condition that the polymer viscosity thermal degradation coefficients are 0,0.0012,0.011, the difference between the width and the depth of the funnel with water is large, and at this time, according to the method of step 2, the corresponding polymer effective concentration decay coefficients are 0,0.001,0.009. As can be seen from FIG. 4, the larger the thermal degradation coefficient of the viscosity of the polymer, the smaller the width and the smaller the depth of the comprehensive water-containing funnel, especially when the thermal degradation of the polymer reaches the condition of FIG. 1, namely, the degradation coefficient is 0.011, the viscosity of the polymer is rapidly reduced about 90 days, and in addition, various shearing actions of the polymer in a shaft and an oil reservoir can be seen in numerical simulation, the polymer can hardly be used for oil displacement, which shows that the method can effectively reflect the influence of the thermal degradation of the polymer on the viscosity of a displacement phase under the high-temperature condition, thereby effectively reflecting the influence of the thermal degradation on the oil displacement effect and the oil displacement index, and providing necessary technical means for the prediction and optimization of a development scheme and even the evaluation and screening of the performance of the polymer.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.